Search for $CP$ violation using $T$-odd correlations in $D_{(s)}^{+}\to K^{+}{K}^{-}\ddot{I}{€}^{+}\ddot{I}{€}^0$, $D_{(s)}^{+}\to K^{+}\ddot{I}{€}^{-}\ddot{I}{€}^{+}\ddot{I}{€}^0$, and $D^{+}\to K^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{+}\ddot{I}{€}^0$ decays

Abstract

We search for $CP$ violation using $T$-odd correlations in five $D_{(s)}^{+}$ and $D_{(s)}^{-}$ four-body decays. Our analysis is based on 980 $\mathrm{f}{\mathrm{b}}^{-1}$ of data collected by the Belle detector at the KEKB energy-asymmetric $e^{+}{e}^{-}$ collider. Our results for the $T$-odd $CP$-violating parameter $a_{CP}^{T\text{-odd}}$ are: $a_{CP}^{T\text{-odd}}(D^{+}\to K^{-}{K}^{+}\ddot{I}{€}^{+}\ddot{I}{€}^0)=(+2.6\pm 6.6\pm 1.3)\times 10^{-3}$, $a_{CP}^{T\text{-odd}}(D^{+}\to K^{+}\ddot{I}{€}^{-}\ddot{I}{€}^{+}\ddot{I}{€}^0)=(-1.3\pm 4.2\pm 0.1)\times 10^{-2}$, $a_{CP}^{T\text{-odd}}(D^{+}\to K^{-}\ddot{I}{€}^{+}\ddot{I}{€}^{+}\ddot{I}{€}^0)=(+0.2\pm 1.5\pm 0.8)\times 10^{-3}$, $a_{CP}^{T\text{-odd}}(D_s^{+}\to K^{+}\ddot{I}{€}^{-}\ddot{I}{€}^{+}\ddot{I}{€}^0)=(-1.1\pm 2.2\pm 0.1)\times 10^{-2}$, and $a_{CP}^{T\text{-odd}}(D_s^{+}\to K^{-}{K}^{+}\ddot{I}{€}^{+}\ddot{I}{€}^0)=(+2.2\pm 3.3\pm 4.3)\times 10^{-3}$, where the uncertainties are statistical and systematic, respectively. These results are the first such measurements and are all consistent with zero. They include the first measurement for a $D_s^{+}$ singly Cabibbo-suppressed decay, and the first measurement for a $D$ meson doubly Cabibbo-suppressed decay. We also measure $a_{CP}^{T\text{-odd}}$ in different subregions of phase space, where the decays are dominated by different intermediate resonance states such as $D^{+}\to \ddot{I}•\ddot{I}{}^{+}$, ${\bar{K}}^{\ast 0}{K}^{\ast +}$, and ${\bar{K}}^{\ast 0}\ddot{I}{}^{+}$; and $D_s^{+}\to K^{\ast +}\ddot{I}{}^0$, $K^{\ast 0}\ddot{I}{}^{+}$, $\ddot{I}•\ddot{I}{}^{+}$, and ${\bar{K}}^{\ast 0}{K}^{\ast +}$. No evidence for $CP$ violation is found.

10 pages, 5 figures